Statistical pattern analysis methods of partial discharge measurements in high voltage insulation

ABSTRACT

Statistical methods of partial discharge analysis utilizing histogram similarity measures are provided by quality assessment and condition monitoring methods of evaluating high voltage electrical insulation. The quality assessment method is utilized to evaluate the quality of insulation within the electrical equipment. The condition monitoring method is utilized during normal operation of the equipment to identify degradation in the insulation and to predict catastrophic insulation failures.

This application is a division of application Ser. No. 08/837,932, filedApr. 11, 1997 now U.S. Pat. No. 6,088,658, which is hereby incorporatedby reference in its entirety.

BACKGROUND OF THE INVENTION

This invention relates to quality assessment and condition monitoring ofelectrical insulation and more particularly to statistical patternanalysis and diagnostics of partial discharge measurements of highvoltage insulation.

Partial discharge (PD) analysis has been established as a usefuldiagnostic tool to asses high voltage insulation systems for integrityand design deficiencies. Interpretation of the PD patterns can revealthe source and the reason for the PD pattern occurrence, and therefore,has been used as a condition monitoring and quality control tool by themanufacturing industry. Analysis of PD patterns for high voltageelectrical equipment has often times been an heuristic process based onempirical reasoning and anecdotal information. This is particularly truefor insulation systems encountered in high voltage rotating machinery.Typically high voltage insulation is a heterogeneous compositecomprising tape, mica flakes, and resin. No insulation system is perfectand there is a statistical distribution of voids and other defectsthroughout the insulation system. This void distribution results in abaseline level of PD activity for all insulation systems. The associateddischarge phenomena are often complicated, multi-faceted events.Discerning between “normal” and defective insulation systems oftenrequire more than simple trending of discharge levels.

For many years, the use of PD results for insulation was impracticablebecause of the difficult data manipulation problems presented. It isthus desirable to identify defective high voltage electrical equipmentby the analysis of PD events in an effective and economic manner.

Typically, users of expensive high voltage electrical equipment incurextraordinary expenses when the equipment unexpectedly fails. Theability to predict failures of this equipment would enable the equipmentuser to utilize condition-based maintenance techniques to avert suchunexpected failures and associated high costs. Additionally, scheduledmaintenance plans cause users to incur unnecessary costs when equipmentis found to be functioning satisfactorily after the scheduledmaintenance. Therefore, there exists a need to monitor high voltageinsulation when the high voltage equipment is in operation to predictwhen a catastrophic defect will occur so as to avoid excessive damageand unexpected and costly repair of the high voltage electricalequipment caused by the defect.

There exists a need to identify when a defect exits in insulation beforeit is placed in the high voltage equipment by assessing the quality ofthe insulation. It is also desirable to identify the type of defect inthe insulation after it is detected.

SUMMARY OF THE INVENTION

The present invention addresses the foregoing needs by providing asystem for evaluation of the insulation system of high voltageequipment, including quality assessment and condition monitoring.

The quality assessment method includes extracting representative qualityclass thresholds from partial discharge (PD) measurements of knowninsulation quality during a training stage. These quality classrepresentatives and quality class thresholds from the baseline are usedfor comparison to analysis features of partial discharge test data toassess the quality of undetermined insulation. Histogram similaritymeasures are utilized to determine the representatives of the qualityclass thresholds of each insulation quality type.

The condition monitoring method includes collecting periodic PDmeasurements of insulation during the normal operation of high voltageequipment. Trend analysis is employed to identify any deviation from anexpected baseline of high voltage electrical equipment.

BRIEF DESCRIPTION OF THE DRAWINGS

The features of the invention believed to be novel are set forth withparticularity in the appended claims. The invention itself, however,both as to organization and method of operation, together with furtherobjects and advantages thereof, may best be understood by reference tothe following description in conjunction with the accompanying drawingsin which like characters represent like parts throughout the drawings,and in which:

FIG. 1 is an illustration of a two dimensional phase resolved PD plotutilized in this invention.

FIG. 2 is an illustration of the voltage cycle over which a PDmeasurement is taken.

FIG. 3 is an illustration of a one dimensional PD plot utilized in thisinvention.

FIG. 4 is a illustration the major steps of the quality assessmentmethod of this invention.

FIG. 5 is an illustration of the major steps of the training step of thequality assessment method.

FIG. 6 is an illustration of the major steps of the testing step of thequality assessment method.

FIG. 7 is an illustration of the test configuration for making PDmeasurements during the quality assessment method.

DETAILED DESCRIPTION OF THE INVENTION

In this Specification, two data analysis methods are presented forintelligent characterization and interpretation of partial discharge PDpatterns including: a statistical classification method utilizinghistogram based analysis to analyze the quality of an insulation system;and a statistical trending method utilizing histogram analysis for thecondition monitoring of insulation systems.

High voltage equipment includes for example, high voltage generators,motors, transformers, and transmission lines.

As illustrated in FIG. 1, the PD measurement is presented in a twodimensional PD plot 10 in which the horizontal axis 26 is delineated bya predetermined number of phase windows 28 and the vertical axis 34 isdelineated by the magnitude of each PD event set 22 measured inpico-farads 32. Two dimensional PD plot 10 is phase resolved, that is,PD event set 22 is taken at predetermined intervals or phase windows 28in correspondence with a single voltage cycle 20.

During the quality assessment method, a set of PD reference measurementdata 324 (FIG. 4) are acquired from high voltage equipment havingvarious known defects and from equipment having no defects. Arepresentative PD measurement is extracted from each of these referencemeasurements and a respective histogram threshold value that is utilizedto identify defects and defect types is determined by computing thehistogram similarity distance between the undetermined insulation andthe representative PD measurements within the reference PD data set. Therespective histogram threshold value 418 and the representative PDmeasurement are then stored in a data base 416 to be used as baselinesfor insulation of undetermined quality. When undetermined high voltageinsulation is tested, PD measurements 322 are acquired and compared todata from reference PD data 324, and a statistical distance differenceis calculated. If the statistical distance is less than histogramminimum threshold value 418 the high voltage insulation is identified asbeing within normal operating parameters, hereinafter referred to as“healthy.” Otherwise, it is identified as defective high voltageinsulation.

During condition monitoring, analysis test data 322 are acquiredperiodically and consecutive measurements are compared using a histogramsimilarity measure. If there is a significant deviation in the histogramsimilarity measure as compared to the measurements acquired in the past,the algorithm generates a indication in correspondence with thedegradation in the insulation system. The amount of the deviation in thenewly acquired histogram similarity measure may be correlated with theseverity of the degradation in the insulation system.

1(a) Histogram Type Measures

In both the quality assessment and condition monitoring methodshistogram similarity measures are utilized. PD measurements 22 aregrouped by phase window 28 with respect to one cycle of source voltage20 in phase resolved PD measurement data. For example, one cycle ofsource voltage 20 is a single cycle of a sixty hertz signal asillustrated in FIG. 2. The single cycle of source voltage 20 is dividedinto the preselected number of phase windows 28. For example,. whentwo-hundred-fifty-six phase windows are selected, each phase window 28is represented by approximately 1.4 degrees of source voltage phase.Each phase window 28 collects respective PD measurement data 64, 66, and68 for about thirty seconds of voltage cycles corresponding with itsrelative position within source voltage 20. This data forms the basis ofa histogram footprint.

A one dimensional histogram has as its horizontal axis the PD magnitudein pico-farads 34 and the vertical axis as the PD event count 33 asillustrated in FIG. 3. PD event set 22 is plotted in the one dimensionalhistogram. Phase resolved PD plot 10 is illustrated as a collection ofthese one dimensional histograms.

Alternatively, only the total number of occurrences need be evaluatedfor each phase window 28 or PD magnitude 34, i.e., the sum of individualPD events 22 for each phase window 28 or for each PD magnitude 34. Thehistogram obtained by the sum of the individual PD events 22 for eachphase window 28 is the phase marginal histogram or X-marginal histogram,and the histogram obtained by the sum of the individual PD events foreach PD magnitude is the magnitude marginal histogram or Y marginalhistogram.

1(b) Histogram Similarity Measures

The following histogram similarity measures are utilized by way ofexample and not limitation, to process the previously describedhistograms: (1) Sample correlation, (2) Kolmogorov-Simimov distance, and(3) Chi-square test.

To simplify the discussion, these measures shall be described for onedimensional histogram 150. The two dimensional description is a simpleextension of several one dimensional histograms.

The normalized joint probability mass function of phase windows 28 andPD magnitudes is computed by dividing the histogram into the total unitarea. The Probability Mass Function or Normalized Histogram is definedby equation 1 below. $\begin{matrix}{{{P(i)} = \frac{h(i)}{A}},{i = 1},\ldots \quad,N,} & (1)\end{matrix}$

where h(i) is the number of events whose intensity is “i”, “A” is thetotal number of events in the observation set, and “N” is the number ofphase windows 28 over a single voltage cycle.

The Cross Correlation value “cr” as defined in equation 2 below:$\begin{matrix}{{{cr} = \frac{\sum\limits_{i = 1}^{N}{\left( {{P_{1}(i)} - \mu_{1}} \right)\quad \left( {{P_{2}(i)} - \mu_{2}} \right)}}{\sqrt{\sum\limits_{i = 1}^{N}{\left( {{P_{1}(i)} - \mu_{1}} \right)^{2}{\sum\limits_{i = 1}^{N}\left( {{P_{2}(i)} - \mu_{2}} \right)^{2}}}}}},} & (2)\end{matrix}$

where μ_(i) is the mean value of probability mass function P(i).

The Kolmogorov-Simimov Distance is calculated using the CumulativeDistribution function, the Kolmogorov Simirnov distance 1 function, andthe Kolmogorov Simirnov distance 2 function.

The Cumulative Distribution Function is defined by equation 3 below:$\begin{matrix}{{{H(k)} = {\sum\limits_{i = 1}^{k}{P(i)}}},} & (3)\end{matrix}$

where H_(i)(k) is the probability that the intensity “i” is less than orequal to k.

The Kolmogorov Simimov distance 1 between two cumulative distributionsis defined by equation 4 below:

$\begin{matrix}{{{KS1} = {\max\limits_{k}{{{H_{1}(k)} - {H_{2}(k)}}}}},} & (4)\end{matrix}$

The Kolmogorov Simirnov distance 2 is defined by equation 5 below:$\begin{matrix}{{KS2} = {\sum\limits_{k = 1}^{N}{{{{H_{1}(k)} - {H_{2}(k)}}}.}}} & (5)\end{matrix}$

Alternatively, the Chi-Square Test is utilized to calculate thenormalized histogram. The Chi-square statistic is described as follows:$\begin{matrix}{{\chi^{2} = {{\sum\limits_{i = 1}^{N}{\frac{\left( {{h(i)} - {{AP}(i)}} \right)}{{AP}(i)}{\sum\limits_{i = 1}^{N}p_{i}}}} = {{1.\quad N_{i}\quad i} = 1}}},\ldots \quad,N} & (6)\end{matrix}$

where P(i) is a known probability mass, and h(i)′ is the number ofevents at intensity “i”, where${\sum\limits_{i = 1}^{N}{h(i)}} = {A.}$

It is desirable to know whether h(i)'s are drawn from the populationrepresented by the P(i)s. If the h(i)'s are drawn from the populationrepresented by P(i)s, then as A→∞, each term in the summation of theequation (6) is the square of a Gaussian random variable with zero meanand unit variance. Therefore, x² is a random variable with Chi-squaredistribution. A large value of x², for example, x²>>N, indicates that itis rather unlikely that the h(i)'s are drawn from the populationrepresented by P(i) because Pr(x²>C|N) is very small.

Pr(x²>C|N) is the probability that the Chi-square statistic is at least“C”, given that there are “N” phase windows 28, alternatively calledbins, in the histogram and that h(i)'s are drawn from the populationrepresented by P(i)s. The value of Pr(x²>C|N) is computed by theincomplete gamma function below: $\begin{matrix}{{\Pr \left( {\chi^{2} > C} \middle| N \right)} = {\frac{\int_{C/2}^{\infty}{^{- x}x^{{N/2} - 1}}}{\int_{C/2}^{\infty}{^{- x}x^{{N/2} - 1}}}.}} & (7)\end{matrix}$

The Chi-Square test for two histograms is described next. Since theprecise probability mass functions of PD event set 22 is notascertainable, what is implemented is a modified Chi-square test whichchecks whether two measurements h₁(i), i=1, . . . , N, and h₂(i), i=1, .. . , N are drawn from the same population by a predeterminedprobability distribution function. In this case the Chi-square statisticis given by: $\begin{matrix}{{\chi^{2} = {\sum\limits_{i = 1}^{N}\frac{\left( {{\sqrt{A_{2}/A_{1}}{h_{1}(i)}} - {\sqrt{A_{1}/A_{2}}{h_{2}(i)}}} \right)}{{h_{1}(i)} + {h_{2}(i)}}}}{{{where}\quad {\sum\limits_{i = 1}^{N}{h_{1}(i)}}} = {{A_{1\quad}{and}\quad {\sum\limits_{i = 1}^{N}{h_{2}(i)}}} = {A_{2}.}}}} & (8)\end{matrix}$

In this implementation, h₁(i) is the first histogram, and h₂(i) is thesecond histogram of PD measurements. Note that if h₁(i)=h₂(i)=0 for somephase window “i”, then the corresponding term is dropped in thesummation in equation (8).

2. Quality Assessment

The quality assessment method is a “supervised” approach, that is, thetype and the number of reference quality classes, against which theinsulation of high voltage equipment is tested, are predetermined. It isutilized for detection, as well as the identification of referencequality classes. Detection involves automatic decision making todetermine whether high voltage equipment has “healthy” or “defective”insulation. Identification, on the other hand, involves defectdetection, as well as, classification of the defect to one of the knownquality classes.

As more information is provided to the system, better inference of thequality of the insulation can be achieved. For instance, for defectdetection, only a set of PD measurements representing a “healthy”insulation system is needed. For quality class identification, however,PD measurements from each quality class are needed. The following list,for example, is a group of quality classes that are detected including:suspended metal particles in insulation; armor degradation; conductorand insulator delamination; insulator/insulator delamination; andinsulator/armor delamination. A list of these failures are illustratedin Table 1. The outcome of such a quality assessment utilizing thepresent invention generates one of these three associated quality classgroup indications, “healthy” insulation, “defective” insulation of knownquality class, and “defective” insulation of undetermined quality class.As more quality classes are programmed into the reference set of detecttypes the identification capability of the system improves.

The quality assessment method comprises four stages including:pre-processing 326, reference 314, testing 316, and post-processing 318as illustrated in the flow diagram in FIG. 3. In pre-processing stage312, PD reference data 324 may be subjected to signal conditioningmethods, such as gain normalization, phase synchronization andexcitation noise suppression. In reference stage 314, thecharacteristics of the defected and good insulation are learned andmemorized from reference data 324. The learning process involvesextraction of the characteristics or quality class features fromreference data 324 and statistical analysis of the quality classfeatures. Statistical analysis of the quality class features leads to aset of quality class representatives 420 for the quality class featuresand an optimal decision making rule 414 as illustrated in FIG. 5. Usingthe reference data and the decision rule, quality class thresholds 418is calculated for each quality class feature. Finally, a respectivequality class representative 420 of each quality class along with arespective quality class thresholds 418 is stored in data base 416 foruse during testing stage 316. In testing stage 316, respective qualityclass features 452 are extracted from a each test bar and a statisticaldistance between quality class representative 420 of each respectivequality class and the quality class features is computed. The resultingrespective distance 456 is compared with respective quality classthresholds 418 in data base 416 to assign the test measurement to one ofthe quality classes stored in data base 416. In post-processing stage318 results from multiple PD measurements are combined to increase theconfidence level and a probability is associated with each decision toquantify the accuracy of the process. Each of the four qualityassessment stages is discussed in more detail below.

2.(a) Pre-Processing

In prepossessing stage 326, reference data 324 and analysis test data322 may be conditioned in any one of the following ways or incombination with multiple sets of the following ways: a) to convert frombipolar data to uni-polar data; b) to phase synchronize with supplyvoltage 20; c) to be normalized with respect to a gain factor; and d)digital filtering may be utilized to suppress the excitation noise inreference data 324 and analysis test data 322.

2.(b) Training

The flow diagram of the training process 314 is illustrated in FIG. 5.Low count high magnitude PD events contain more discriminativeinformation than the low magnitude high count PD events. In oneembodiment of the feature extraction process, the logarithm of the PDevent counts is calculated. In addition the effect of high count lowmagnitude events may be suppressed by setting a predeterminedlower-level PD magnitude threshold discarding data below this value.Typically, the lower-level PD magnitude threshold is the bottom tenpercent of the PD magnitude range.

Respective quality class representatives 420 from each quality class isextracted by averaging reference data 324. Expressed mathematically letR_(i) denote the quality class representative 420 of the quality class iand P_(i) ^(j) be the “jth” member of the quality class “i.” Next, anintra quality class distance between its quality class representative420, R_(i), and each of its member, R_(i) ^(j), in reference data set324 is calculated by using the histogram similarity measures introducedabove.

D _(i) ^(j) =d(P _(i) ^(j) ,R _(i))  (9)

where d is the histogram similarity measure. Note that in the case of 1Dhistogram similarity measures, the distance function is a vector inwhich each entry is the distance between the member and reference 1Dhistograms of respective phase window 28. To clarify this difference,vector notation for the 1D histograms is introduced:

D _(i) ^(j)(ω)=d(P _(i) ^(j)(ω),R _(i)(ω)), ω=1, . . . , L.  (10)

ω corresponds to the phase window 28, and the value L was selected basedon the number of phase windows 28 over a single cycle of source voltage20 as discussed above.

In order to obtain an optimal radius for each quality class, the samplemean and standard deviation of the distances within each quality classare calculated. For 2D histograms the intra quality class mean radiusand standard deviation are given as follows: $\begin{matrix}{{\overset{\_}{D}}_{i} = {\frac{1}{N_{i}}{\sum\limits_{j = 1}^{N_{i}}D_{i}^{j}}}} & (11) \\{\sigma_{i} = \sqrt{\frac{1}{N_{i}}{\sum\limits_{j = 1}^{N_{i}}\left( {D_{i}^{j} - {\overset{\_}{D}}_{i}} \right)^{2}}}} & (12)\end{matrix}$

where N_(i) is the number of samples available for the quality class“i.” For the 1D phase resolved histograms the intra-class mean radiusand standard deviation are given by $\begin{matrix}{{{\overset{\_}{D}}_{i}(\omega)} = {\frac{1}{N_{i}}{\sum\limits_{j = 1}^{N_{i}}{D_{i}^{j}(\omega)}}}} & (13) \\{{{\sigma_{i}(\omega)} = \sqrt{\frac{1}{N_{i}}{\sum\limits_{j = 1}^{N_{i}}\left( {{D_{i}^{j}(\omega)} - {{\overset{\_}{D}}_{i}(\omega)}} \right)^{2}}}},{\omega = 1},\ldots \quad,{L.}} & (14)\end{matrix}$

Next, an α unit standard deviation tolerance is allowed for each qualityclass radius. Note that in the case of Gaussian distribution of theintra-class distances, α is typically chosen to be two to provide a 99%confidence interval. The quality class radius, for the respective 2D and1D histograms are given as follows:

τ_(i) ={overscore (D)} _(i)+ασ_(i)  (15)

$\begin{matrix}{{\tau_{j} = {{\sum\limits_{\omega = 1}^{256}{{\overset{\_}{D}}_{i}(\omega)}} + {{\alpha\sigma}_{i}(\omega)}}},{\omega = 1},\ldots \quad,{L.}} & (16)\end{matrix}$

Finally, for each quality class {R_(i), τ_(i)} are stored in the database as quality class representative 420 and the quality class threshold418 of each quality class.

2.(c) Testing

The major steps of testing stage 316 is illustrated in FIG. 6. Analysistest data 322 is utilized in the following steps. First, analysis testdata 322 are subjected to the steps discussed in pre-processing stage312 prior to extracting the relevant features. Next, the distancebetween the analysis feature, T, and the references of each qualityclass R_(i) are computed using one of the histogram similarity measuresdescribed above. For the 2D histogram, the distance is given by a scalarquantity (equation 17) while for the 1D histogram similarity measures,it is given by a vector quantity (equation 18):

Δ_(i) =d(T,R _(i)) i=1, . . . , C  (17)

Ω_(i)(ω)=d(T(ω),R _(i)(ω)), ω=1, . . . , L, i=1, . . . , C  (18)

where “C” is the number of quality classes. In order to compare thevector quantity identified in equation (18), with quality classthreshold 418, a cumulative distance is computed by summing the quantityin equation (18) over the phase windows 28: $\begin{matrix}{\Delta_{i} = {\sum\limits_{\omega = 1}^{L}{\Omega_{i}(\omega)}}} & (19)\end{matrix}$

Next, the respective distance between the analysis features and qualityclass representative 420 of each quality class, Δ_(i), are calculated.If the distance is greater than all quality class thresholds 418, thetest measurement is tagged as “defective.” However, the quality class isnot one of the types for which the algorithm is trained to recognize. Ifthe distance is less than one or more quality class thresholds 418, thetest measurement is assigned to the quality class to which the distancebetween the associated reference and analysis feature is minimum. If thefinal assignment is the quality class of healthy insulation, themeasurement is tagged as “healthy.”

To improve the accuracy of this quality class assignment, testing stage316 is repeated for multiple sets of analysis test data 322. Decisionsobtained for each set of analysis test data 322 and distances of eachfeature to each quality class representative 420 are then subjected topost-processing 318 to finalize the decision of each undeterminedinsulation system.

2.(d) Post-Processing

In post-processing stage 318, there are two major tasks: first, thedecisions in testing stage 316 are combined; second, a probability isassociated to each decision to reflect the accuracy of the qualityclassification.

The distance of the analysis feature to a quality class as illustratedin equation (17) is quantified in terms of unit standard deviation ofthe quality class. Relative comparison of these distances determines theaccuracy of the final decision. The distances are mapped to aprobability distribution function in order to compare these decisions.If the distance between the analysis feature and the quality class iszero, or significantly larger, such as α², The classification decisionis about 100% accurate. In the case of zero distance, analysis test dataset 322 belongs to the quality class with probability 1. In the case ofα² or larger distances, the probability that analysis test data set 322belongs to the quality class is zero. The difficulty arises whenassigning a probability to the distances that are between zero and α².To resolve this issue, equation (20) is used between the distance andprobability spaces. $\begin{matrix}{{f(\Delta)} = \left\{ \begin{matrix}\left( {1 - \frac{\Delta}{\gamma}} \right)^{- \beta} & {0 \leq \Delta < \gamma} \\0 & {\Delta \geq \gamma}\end{matrix} \right.} & (20)\end{matrix}$

Note that when the distance is zero, i.e., Δ=0, the probability, f(Δ),is 1, and when the distance is greater or equal to γ, the probability iszero.

Two parameters in equation (20) are user-controlled, namely γ and β. Theparameter γ controls the threshold beyond which the probability that ameasurement coming from a particular quality class has distance γ orlarger. This distance can be set to an order magnitude larger than thethreshold α, such as α² unit standard deviation. The parameter βcontrols the confidence in quality class identification power of thetesting scheme. This parameter is preselected so that 80% or more valuesshould be correctly classified. If a value is chosen at the 80% qualityclass identification level, β is given as follows:

β==In0.8/In(1−α/γ)  (21)

Or more generally, choose β so that f(α) is equal to the confidencelevel defined as a probability percentage. For example, when f(Δ), isselected to be 80% γ, may be selected to be four and β is calculated tobe −0.322. These parameters enable a quality class likelihood to beassigned each analysis test data set 322. Other values for equation (20)may also be selected.

While probability mapping functions defined in equations (20) and (21)are utilized in this invention, any technique can be utilized to producethe above results, for example, a computer look-up table, or a set oflogical rules defined in a computer program.

Next, the quality class assignments and the associated probabilityvalues are combined to get a final quality class assignment and aprobability value for analysis test data set 322. The steps of thisprocess are summarized as follows:

A probability value is assigned to each analysis test data set 322describing the likelihood of the measurement belonging to each qualityclass in the database. Let p_(i) ^(j), j=1,. . . , M and i=1, . . . , Nbe the probability that the measurement j belongs to quality class i.where “M” is the total number of measurements.

Next, {overscore (p_(i)+L )} is defined as the probability that theanalysis test data set 322 representing a test bar belongs to qualityclass i with probability {overscore (p)}_(i). $\begin{matrix}{{{\overset{\_}{p}}_{i} = {\frac{1}{M}{\sum\limits_{j = 1}^{M}p_{i}^{j}}}},{i = 1},\ldots \quad,C} & (22)\end{matrix}$

The insulation represented by analysis data set 322 is next assigned tothe quality class with the highest overall probability, i.e.,

î=Argmax/i {overscore (p)} _(i)  (23)

where Argmax is the quality class at which {overscore (p)}_(i), i=1, . .. N is maximum.

An example of the above described quality assessment method, ispresented. Several quality class classes of generator stator bars,hereinafter described as bars or generator bars, were programmed intothe statistical model as several respective reference data sets 324.Next, undetermined generator bars were evaluated based on respectivereference data set 324. The results are described and illustrated below.

Several types of stator bar defects or quality classes were investigatedincluding suspended metallic particles in the insulation, slot armordegradation, corona suppresser degradation (i.e., the external voltagegrading), insulation-conductor delaminations, insulator-insulator(bound) delaminations, and “white” insulation. Each of these qualityclass has implications for either quality assessment or conditionmonitoring either during production or during service Each bar wassubjected to a specific sequential set of events to ensure consistentreliable PD data.

The typical test configuration is illustrated in FIG. 7. A 60 Hz,corona-free, supply voltage 20 having an associated impedance 477energizes respective model generator stator bars 489. Respective statorbars 489 are placed in simulated stator slots 487 and 485 and heldfirmly. Slots 487 and 485 are made of either aluminum or steel platescut to fit the slot section of stator bars 489. A 1.3 nano-farad ceramiccoupling capacitor 491 is used as a coupling impedance which allows PDcurrent 483 to pass through current transformer 481 coupled thereto. Thebandwidth of data collection is 100,000 to 800,000 Hertz. Data iscollected for thirty seconds for each PD pattern. Multiple, sequentialpatterns are collected for each respective stator bar 489.

The results of the quality assessment approach for various histogramtype similarity measures is next presented as an example of theoperation of the quality assessment approach. This example includescomparison of the 2D Chi-square, correlation, and Kolmogorov-Simimovmethods of statistically analyzing PD data. The number of test samplesand type of reference quality classes used for each quality class istabulated in Table 1. For quality class matching, both the linear andthe logarithmic-scaled PD data were used.

TABLE 1 Number of Testing Samples for each Quality Class Number Qualityof class Measurements Good Bar 10 Suppresser 5 Metal Wires 5 No Int 10Grade Cu Delam 5 Whitebar 5 Therm & 4 VE Arm 4 Control Slot Dischg 4

In this example, there are a total nine quality classes, eight fordefects and one for “healthy” insulation. Fifty-two patterns werecollected. The respective reference data sets 324 and respective qualityclass thresholds 418 are determined for each quality class andsimilarity measure. Quality class thresholds 418 of the correlationmethod for each quality class are tabulated in Table 2 for both a linearand a logarithmic treatment of the patterns. The linear thresholds arecalculated when data from the PD magnitude 34 (FIG. 1) is a linearscale. The logarithmic threshold are calculated based on a logarithmicPD magnitude 34.

TABLE 2 Correlation Thresholds for each Quality class Linear LogarithmQuality Threshold icThreshol class s ds Good Bar 0.93 0.97 Suppresser0.79 0.96 Metal Wires 0.95 0.97 No Int 0.87 0.96 Grade Cu Delam 0.980.98 Whitebar 0.98 0.98 Therm & 0.58 0.98 VE Arm 0.88 0.98 Control SlotDischg 0.97 0.95

The “quality class detection” and “quality class identification” powerof each histogram similarity measure was determined. Defect detectionpower is defined as the “probability of detecting” the presence of adefect. “Identification power” is the probability of identifying thequality class correctly. A “false positive” is a quality classidentification when no quality class should have been identified. Theseresults are summarized in Table 3.

TABLE 3 Performance of the Testing Stage Using 1D Phase Histograms TestType Defect Detection False Positive Defect ID Chi-squares 100% 70% 78%Correlation 100% 0% 96% Kolmogorov-Simirnov 1 100% 0% 96%Kolmogorov-Simirnov 2 100% 0% 98%

A preferred embodiment of conducting the histogram similarity analysisis to use the 1D phase Kolmogorov-Simimov 2 approach because the itprovides the best measure in quality class detection and quality classidentification as is illustrated in Table 3. Out of fifty-five patternsets acquired from the defective bars all of them were correctlyidentified as defective yielding a 100% defect detection confidencelevel as is illustrated in Table 4. On the other hand, fifty-five of thefifty-six patterns are correctly identified yielding 98% classidentification confidence.

The detailed experimental results for the 1D phase Kolmogorov-Simirnov 2test are summarized in the confidence matrix illustrated in Table 4. Thenumber in the “ith” row and “jth” column of this table shows how manysamples from quality class “i” is classified to quality class “j”. Forexample the row titled “No Int grade” or No internal grading shows thatonly one sample is miss-classified as quality class “Cu Delam” or Copperdelamination degradation while nine samples are correctly classified asthe quality class “No Int grade.”

TABLE 4 Confidence Matrix for the Kol-Simiornov 2 Test Using 1D PhaseHistogram Supr- Metal No Int Cu White Therm& Slot Am Good essor wiregrade Delam bar VE dischg control bars Supressor 5 Metal wire 5 No Intgrad 9 1 Cu Delam 5 Whitebar 5 Therm&VE 4 Slot dischg 4 Arm control 4Good bars 10

The 1D phase Kolmogorov-Simimov 1 method provides similar results as the1D phase Kolmogorov-Simimov 1 method (Table 5). It also has 100% qualityclass detection as indicated in Table 3. The quality classidentification, however, is slightly less at 96%. One test method may bemore adept at identifying quality classes than another method. In tables4 and 5 the 1D phase Kolmogorov-Simimov 2 erred in identifying one nograde and the 1D phase Kolmogorov-Simirnov 1 erred in identifying onebared copper/insulation delamination test. These errors are furthereliminated by employing multiple statistical distance comparisons usingdifferent statistical methods. For example, both the 1D phaseKolmogorov-Simirnov 1 and the 1D phase Kolmogorov-Simirnov 2 can becombined to improve fault identification.

TABLE 5 Confidence Matrix for the Koi-Simiornov 1 Test Using 1D PhaseHistogram Supr- Metal No Int Cu White Therm& Slot Am Good essor wiregrade Delam bar VE dischg control bars Supressor 5 Metalwire 5 No Intgrade 10 Cu Delam 5 Whitebar 1 4 Therm&VE 4 Slot dischg 1 3 Arm control4 Good bars 10

3. Condition Monitoring

The objective of a condition monitoring method is to quantify the healthof the system to predict catastrophic failures, to avoid excessivedamage and unexpected down times, and to allow condition-basedmaintenance. The condition monitoring method acquires PD measurementsperiodically and compares them with past PD measurement to detectstatistical deviations. Any significant deviation in the most currentmeasurement is identified as an indication of change in the PD activityof the high voltage insulation.

The condition in which the measurements remain statistically unchangedis hereinafter identified in this Specification as a “steady statecondition.” In a typical generator with a healthy insulation system, asteady state condition lasts about 3 to 6 months. While the measurementsin each state remain unchanged, they follow a time dependent trend lineover several steady states. The underlying truism in conditionmonitoring and failure detection system is that the measurements duringa pre-catastrophic state do not match to the predicted values obtainedfrom the trend analysis of the earlier states, because catastrophicdeterioration is expected to be revealed by the rate of increase in thePD activity. The implementation of the condition monitoring methodinvolves the following steps: 1) preprocessing as discussed above; 2)feature extraction as discussed above; 3) establishing a parametrictrend model; 4) estimating the trend parameters; 5) and, predicting thePD trend so as to detect pre-catastrophic failures.

By way of example, and not limitation the “steady state condition” of ahigh voltage machine is about six months and the data are collectedevery week on full load operation. Due to external operating conditionsand the physical nature of the PD activity, there are variations andnoise in day to day PD measurements. To suppress noise, the seven day PDmeasurement is averaged on a weekly basis. PD measurements are taken atthe full load condition of the high voltage electrical equipment. Toquantify the daily fluctuations, the distance between the weekly averageand the daily measurements is measured. Next, a monthly average iscalculated based on four weekly averages. Then weekly fluctuations arecalculated based on the monthly average. These fluctuations provideinformation about the short term behavior of the PD activity. Theaverage value of these fluctuations is expected to be a constant as longas the equipment is not in a pre-catastrophic state. Next, measure thesimilarity of the weekly and monthly averages to a predeterminedprevious step.

PD measurements for condition monitoring typically are taken atpreselected intervals that depend on the expected rate of insulationdeterioration, as such, the weekly and monthly intervals may be anyother interval of time.

Statistical analysis used to determine the predicted catastrophicfailure is based on condition monitoring is as follows.

Let P_(i) ^(m) and P_(i) ^(w) represents the monthly and weekly averagePD measurements. Let D^(m)(τ) and D^(w)(τ) be the distance between τapart measurements, i.e.,

D ^(m)(τ)=d(P _(i) ^(m) , P _(i+τ) ^(m))  (24)

and

D ^(w)(τ)=d(P _(i) ^(w) , P _(i+τ) ^(w))  (25)

where the distance d is one of the histogram similarity measuresintroduced previously. Typically, the distance between the measurementsincreases as the time lag τ increases. Therefore, the distance valuesconform to trend line models of the form:

D ^(m)(τ)=A ^(m) τ+B ^(m)+{square root over (ρ^(m)+L )}N ^(m)(τ), τ=1,2, 3, . . . T  (26)

and

D ^(w)(τ)=A ^(w) τ+B ^(w)+{square root over (ρ^(w)+L )}N ^(w)(τ), τ=1,2, 3, . . . T  (27)

where N^(m)(τ), N^(w)(τ), τ=1, 2, 3, . . . T are Gaussian zero mean unitvariance white noise processes and p^(m) and p^(w) are the variance ofD^(m)(τ) and D^(w)(τ) respectively. “T” is a number representing apredetermined number of PD measurements before the latest PDmeasurement. For example, “T” may be five steps from the latest measuredstep. While equations (26) and (27) are expressed as linear models,other models may be utilized such as a hyperbolic model or log linearmodel of the form presented in equations (28) and (29) respectively.

D ^(m)(τ)=τ^(α) ^(m) +β^(m)+{square root over (δ^(m)+L )}N ^(m)(τ), τ=1,2, 3, . . . T  (28)

and

D ^(w)(τ)=τ^(α) ^(w) +β^(w)+{square root over (δ^(w)+L )}N ^(w)(τ), τ=1,2, 3, . . . T  (28)

Note that both the parameter A and the parameter α control the rate atwhich the partial discharge activity changes. While A quantifies a firstorder polynomial change, α quantifies a change faster than anypolynomial but less than an exponential change. The parameter whichcontrols the rate of increase as identified by parameter A and parameterα is identified as the “trend rate.” The parameter B and the parameter βdetermine the constant difference between consecutive PD measurements.The parameter B and the parameter β is identified as the “trendconstant.” The variance of the process as is identified as the “trendvariance.” The condition during which the trend rate is constant shallbe identified as the “steady state condition.” The “trend rate” and the“trend variance” of the weekly and monthly averages are expected toincrease indicating normal increased PD activity. However, the increasein these parameters is expected to be linear when the insulation systemis still relatively healthy. Note that if the time difference τ and thedistance D^(w)(τ) are statistically independent, the trend rate estimatewill be about zero.

The discussion that follows is based on the linear monthly model,however, any of the trend line models identified above may besubstituted for the linear monthly model.

3(a) Estimation of the Trend Parameters

The parameters of the model typically is estimated using the linear orlog linear least squares method. For example, the linear monthly modelprovides estimate parameters based on the following formulas:$\begin{matrix}{{\hat{A}}^{m} = \frac{{\sum\limits_{\tau = 1}^{T}{{D^{m}(\tau)}\tau}} - {\frac{1}{T}{\sum\limits_{\tau = 1}^{T}{{D^{m}(\tau)}{\sum\limits_{\tau = 1}^{T}\tau}}}}}{{\sum\limits_{\tau = 1}^{T}\tau^{2}} - {\frac{1}{T}\left( {\sum\limits_{\tau = 1}^{T}\tau} \right)^{2}}}} & (30) \\{{\hat{B}}^{m} = {{\frac{1}{T}{\sum\limits_{\tau = 1}^{T}{D^{m}(\tau)}}} - {{\hat{A}}^{m}\frac{1}{T}{\sum\limits_{\tau = 1}^{T}\tau}}}} & (31) \\{{\overset{\_}{\rho}}^{m} = \frac{\sum\limits_{\tau = 1}^{T}\left( {{D^{m}(\tau)} - {{\hat{A}}^{m}\tau} - {\hat{B}}^{m}} \right)}{T - 2}} & (32)\end{matrix}$

3(b) Predicted Partial Discharge Activity

In order to detect an outstanding state, the “trend rate” must beestimated based on past PD measurements and compared with the PDmeasurement estimated from the new measurements. If the variance of theprocess is known, the “trend rate” estimate is Gaussian withdistribution $\begin{matrix}{{N\left( {{\hat{A}}^{m},{\rho^{m}/\left( {{\sum\limits_{\tau = 1}^{T}\tau^{2}} - \left( {\frac{1}{T}{\sum\limits_{\tau = 1}^{T}\tau}} \right)^{2}} \right)}} \right)}.} & (33)\end{matrix}$

Since the variance of the process is undetermined, the estimate Â^(m) ist-distributed with T−2 degrees of freedom. Therefore the (100−2P)%catastrophic confidence interval is given by $\begin{matrix}{{{{\hat{A}}^{m} - A^{m}}} < {t_{c}\frac{\sqrt{{\hat{\rho}}^{m}}}{\left( {{\sum\limits_{\tau = 1}^{T}\tau^{2}} - \left( {\frac{1}{T}{\sum\limits_{t = 1}^{T}\tau}} \right)^{2}} \right)}}} & (34)\end{matrix}$

where t_(c) is such that for the t-distribution with T−2 degrees offreedom, there is P% chance that t>t_(c). Similarly, for known processvariance the “trend constant” estimate is Gaussian with distribution$\begin{matrix}{{N\left( {B^{m},{\rho^{m}{\sum\limits_{\tau = 1}^{T}{\tau^{2}/{T\left( {{\sum\limits_{\tau = 1}^{T}\tau^{2}} - \left( {\frac{1}{T}{\sum\limits_{\tau = 1}^{T}\tau}} \right)^{2}} \right)}}}}} \right)}.} & (35)\end{matrix}$

For undetermined p^(m), the trend constant estimate is t-distributedwith T−2 degrees of freedom. Therefore a (100−2P)% catastrophicconfidence interval is given by $\begin{matrix}{{{{\hat{B}}^{m} - B^{m}}} < {t_{c}\sqrt{{\hat{\rho}}^{m}{\sum\limits_{\tau = 1}^{T}{\tau^{2}/{T\left( {{\sum\limits_{\tau = 1}^{T}\tau^{2}} - \left( {\frac{1}{T}{\sum\limits_{\tau = 1}^{T}\tau}} \right)^{2}} \right)}}}}}} & (36)\end{matrix}$

where P is a predetermined number to provide a desired confidence level.For example, a “P” value of 0.5 provides a confidence level of 99%. Thepredicted value of the distance, D^(m)(τ₀)=d(P_(i) ^(m), P_(i−τ) ₀^(m)), of a future partial discharge measurement p_(i) ^(m) and thepartial discharge measurement τ₀ steps behind it may be obtained fromthe trend line mode defined in equation (37):

{circumflex over (D)} ^(m)(τ₀)=Â ^(m)τ₀ +{circumflex over (B)}^(m).  (37)

If the variance of the process is known, the predicted value {circumflexover (D)}^(m)(τ₀) has a Gaussian distribution based on the formula inequation (38): $\begin{matrix}{{N\left( {{{A^{m}\tau_{0}} + B^{m}},{\rho^{m}\left\{ {\frac{1}{T} + {\left( {\tau_{0} - {\frac{1}{T}{\sum\limits_{\tau = 1}^{T}\tau}}} \right)^{2}/\left( {{\sum\limits_{\tau = 1}^{T}\tau^{2}} - \left( {\frac{1}{T}{\sum\limits_{\tau = 1}^{T}\tau}} \right)^{2}} \right)}} \right\}}} \right)}.} & (38)\end{matrix}$

The predicted distance {circumflex over (D)}^(m)(τ₀) is t-distributedwith T−2 degrees of freedom. Therefore the (100−2P)% confidence intervalis given by $\begin{matrix}{{{{{\hat{D}}^{m}\left( \tau_{0} \right)} - {D^{m}\left( \tau_{0} \right)}}} < \quad {t_{c}\quad \sqrt{{\hat{\rho}}^{m}\left\{ {\frac{1}{T} + {\left( {\tau_{0} - {\frac{1}{T}{\sum\limits_{\tau = 1}^{T}\tau}}} \right)^{2}/\left( {{\sum\limits_{\tau = 1}^{T}\tau^{2}} - \left( {\frac{1}{T}{\sum\limits_{\tau = 1}^{T}\tau}} \right)^{2}} \right)}} \right\}}}} & (39)\end{matrix}$

Steps of the condition monitoring method are summarized as follows:

Step 1. Collect “Z” number of PD measurements and compute the distanceof the most recent measurements to the τ step back partial dischargemeasurements, for each τ≦T where T is a value less than the number ofmeasurements “Z.”

Step 2. Forming a parametric trend relationship between the distancesD^(m)(τ) and D^(w)(τ) and the time lag τ as illustrated in equations(26) through (29).

Step 3. Estimate the trend parameters as described in equations(33)-(36).

Step 4. Predict the next step of the future partial discharge activityas described in equation (37).

Step 5. Collect the next partial discharge measurement and compute theone step difference as described in equation (24) or (25).

Step 6. Compare the difference between the actual one step distance andthe predicted distance with the value described in equation (39). If theactual one step distance is within allowable limits, update the trendparameter estimation using the new measurement. Otherwise tag themeasurements as a potential indication of the change in the condition ofthe insulation system. Repeat the prediction-comparison procedure for anumber of times to assure an indication of change in the condition ofthe insulation system.

Step 7. Estimate new trend parameters for the new condition.

Step 8. Compare the new “trend rate” and constant with the previous“trend rate” and constant using the equations (34) and (36). If both arebeyond the values described in equations (34) and (36), generate anindication denoting a potential pre-catastrophic condition of themeasured insulation. Repeat the observations to verify thepre-catastrophic condition.

The condition monitoring process as defined in this section provides amethod of monitoring high voltage electrical equipment to predictimmanent catastrophic insulation failures. This invention thus obviatesthe need for condition-based monitoring of electrical insulation withinhigh voltage equipment in service.

It will be apparent to those skilled in the art that, while theinvention has been illustrated and described herein in accordance withthe patent statutes, modifications and changes may be made in thedisclosed embodiments without departing from the true spirit and scopeof the invention. It is, therefore, to be understood that the appendedclaims are intended to cover all such modifications and changes as fallwithin the true spirit of the invention.

What is claimed is:
 1. A statistical method of condition monitoring theinsulation in high voltage equipment utilizing partial dischargemeasurements, comprising the following steps: calculating at least oneanalysis feature of undetermined insulation based on a plurality ofpartial discharge measurements; estimating trend parameters of said atleast one analysis feature based on a linear trend line generated basedon a plurality of previously determined ones of said analysis feature;predicting an estimated analysis feature statistical distance of saidanalysis feature with respect to said trend line; comparing saidpredicted analysis feature statistical distance with an actual analysisfeature statistical distance so as to determine whether the condition ofsaid undetermined insulation has changed.
 2. The statistical method ofcondition monitoring as recited in claim 1 further comprising the stepsof: conditioning said partial discharge measurements for computermanipulation; generating a plurality of partial discharge measurementsfrom said high voltage equipment with undetermined insulation so as tocalculate at least one said analysis feature of said undeterminedinsulation.
 3. The statistical method of condition monitoring as recitedin claim 2 further comprising the steps of estimating said trendparameters of said analysis features based on a parabolic trend linegenerated in correspondence with previously determined ones of saidanalysis features.
 4. The statistical method of condition monitoring asrecited in claim 1 further comprising the steps of estimating said trendparameters of said analysis features based on a parabolic trend linegenerated in correspondence with previously determined ones of saidanalysis features.
 5. The statistical method of condition monitoring asrecited in claim 1 further comprising the steps of estimating said trendparameters of said analysis features based on a log linear-trend linegenerated in correspondence with previously determined ones of saidanalysis features.
 6. The statistical method of condition monitoring asrecited in claim 1 further comprising the step of generating a change incondition signal when the measured statistical distance is outside anormal operating limit.
 7. The statistical method of conditionmonitoring as recited in claim 1 further comprising the steps of:synchronizing the phase of said partial discharge measurements over asingle cycle of a supply voltage; normalizing the partial dischargemagnitude of said partial discharge measurements; and removingexcitation noise from said partial discharge measurements.
 8. Thestatistical method of condition monitoring as recited in claim 7 furthercomprising the step of taking the logarithm of said partial dischargemagnitudes to minimize the low magnitude high partial discharge eventcount.
 9. The statistical method of condition monitoring as recited inclaim 8 further comprising the steps of comparing the latest calculatedsaid trend parameters with the previously calculated ones of said trendparameters.
 10. The statistical method of condition monitoring asrecited in claim 9 further comprising the step of generating apre-catastrophic insulation signal when the difference in a plurality ofprevious ones of said trend parameters and current said trend parametersare greater than a catastrophic confidence interval value.